This paper proposes an algorithm for the numerical simulation of linear structural dynamics problems under unilateral elastic constraints, i.e., constraints with a linear force/displacement characteristic whenever active. The presented procedure relies on an event-driven strategy for the handling of the contact constraints, in combination with one-step schemes dedicated to the time integration of the second-order equations of motion. Efficiency of the procedure follows from the use of cubic Hermite interpolation to continuously extend the normal gap functions that reflect the openings of the contact interfaces. Robustness follows from the proper handling of complex numerical situations, e.g., numerical grazing or discontinuity sticking, through appropriate algorithm structure and numerical implementation. And, integration stability is guaranteed by the very nature of the algorithm and that of the one-step integration scheme. Following a detailed coverage of the integration procedure and the countermeasures to the expected numerical difficulties, three application examples are treated for illustration purposes. A MATLAB implementation of the procedure is provided online; download and usage information are given in the Appendix. [less ▲]

Due to the overall process complexity, studies about percussive drilling usually focus on a limited set of the subprocesses underlying it, e.g., the hammer thermodynamics or the interaction between the ... [more ▼]

Due to the overall process complexity, studies about percussive drilling usually focus on a limited set of the subprocesses underlying it, e.g., the hammer thermodynamics or the interaction between the bit and the rock. Following this paradigm, the assessment of the process performance is typically performed by considering a single percussive activation and a single interaction cycle between the bit and the rock, from arbitrary initial conditions. The need for an integrated approach to evaluate drilling performance, based on the dynamical interaction of the subprocesses underlying drilling, is evident. Such an approach requires simplified models, however, as the computational cost associated with full scale models is simply unbearable. In this thesis, three dynamical integrated models are proposed and a preliminary analysis is conducted for a reference configuration and around it. The models couple three modules that represent: (i) the dynamics of the mechanical system, (ii) the interaction between the bit and the rock, and (iii) the activation of the mechanical system. For each module, simple representations are considered; of particular importance is the bit/rock interaction model which is a generalization to repeated interactions of experimental evidence observed for a single interaction. In the first model, the dynamics of a rigid bit is cast into a drifting oscillator and the activation modeled as a periodic impulsive force. The second and third models account for the dynamics of the piston and the activation results from the impact of the piston on the bit. They are respectively based on elastic and rigid representations of the two bodies. In the rigid model, analytical results of wave propagation in thin rods are used to represent the contact interaction between the piston and the bit. In the elastic model, wave propagation is resolved. Their preliminary analysis has revealed the occurrence of complex dynamical responses in the space of parameters. Expected trends are recovered around a reference configuration corresponding to a low-size hammer, with an increase of the rate of penetration with the feed force and the percussive frequency. The latter is seen to have a strong influence on the rate of penetration. Interestingly, our analyses show that when the activation period has the same order of magnitude as the timescale associated with the bit/rock interaction, a lower power consumption is observed, indicating a possible resonance phenomenon in the drilling system. Also, the predictions of the rigid model are shown to be in good agreement with the ones of the elastic model, in the explored range of parameters. Given the piecewise linear nature of the proposed models, dedicated numerical tools have been developed to conduct their analysis. As such, the thesis proposes a high-order time integration scheme for structural dynamics as well as a novel framework to evaluate the accuracy of such schemes, and a root-solving module to perform event-detection for coupling with event-driven integration strategies. Specific to the framework is the account for both structural damping and external forcing in the evaluation of the scheme order of accuracy. Specific to the root-solving module is the forcing of event occurrence in the localization procedure. [less ▲]